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Euler Load given Final Deflection at Distance X from end A of Column Formula

GoEuler Load Formula

GoEuler Load given Factor of Safety Formula

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Euler load is the compressive load at which a slender column will suddenly bend or buckle. Check FAQs

P E = \frac{P}{1 - (C \cdot \frac{\sin (\frac{π \cdot x}{l})}{δ c})}

P_E - Euler Load?P - Crippling Load?C - Maximum Initial Deflection?x - Distance of Deflection from end A?l - Length of Column?δ_c - Deflection of Column?π - Archimedes' constant?

Euler Load given Final Deflection at Distance X from end A of Column Example

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Here is how the Euler Load given Final Deflection at Distance X from end A of Column equation looks like with Values.

Here is how the Euler Load given Final Deflection at Distance X from end A of Column equation looks like with Units.

Here is how the Euler Load given Final Deflection at Distance X from end A of Column equation looks like.

4000.0002 = \frac{2571.429}{1 - (300 \cdot \frac{\sin (\frac{3.1416 \cdot 35}{5000})}{18.4711})}

4000.0002N = \frac{2571.429N}{1 - (300mm \cdot \frac{\sin (\frac{3.1416 \cdot 35mm}{5000mm})}{18.4711mm})}

4000.0002 = \frac{2571.429}{1 - (300 \cdot \frac{\sin (\frac{3.1416 \cdot 35}{5000})}{18.4711})}

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Euler Load given Final Deflection at Distance X from end A of Column Solution

Follow our step by step solution on how to calculate Euler Load given Final Deflection at Distance X from end A of Column?

FIRST Step Consider the formula

P E = \frac{P}{1 - (C \cdot \frac{\sin (\frac{π \cdot x}{l})}{δ c})}

Next Step Substitute values of Variables

∴

P E = \frac{2571.429N}{1 - (300mm \cdot \frac{\sin (\frac{π \cdot 35mm}{5000mm})}{18.4711mm})}

Next Step Substitute values of Constants

∴

P E = \frac{2571.429N}{1 - (300mm \cdot \frac{\sin (\frac{3.1416 \cdot 35mm}{5000mm})}{18.4711mm})}

Next Step Convert Units

∴

P E = \frac{2571.429N}{1 - (0.3m \cdot \frac{\sin (\frac{3.1416 \cdot 0.035m}{5m})}{0.0185m})}

Next Step Prepare to Evaluate

∴

P E = \frac{2571.429}{1 - (0.3 \cdot \frac{\sin (\frac{3.1416 \cdot 0.035}{5})}{0.0185})}

Next Step Evaluate

∴

P E = 4000.00017553303N

LAST Step Rounding Answer

∴

P E = 4000.0002N

Euler Load given Final Deflection at Distance X from end A of Column Formula Elements

Variables

Constants

Functions

Euler Load

Euler load is the compressive load at which a slender column will suddenly bend or buckle.

Symbol: P_E

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Euler Load

Crippling Load

Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Crippling Load

Maximum Initial Deflection

Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

Symbol: C

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Maximum Initial Deflection

Distance of Deflection from end A

Distance of Deflection from end A is the distance x of deflection from end A.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance of Deflection from end A

Length of Column

Length of Column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Column

Deflection of Column

Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Column

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Euler Load

Go Euler Load

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Go Euler Load given Factor of Safety

P E = \frac{P}{1 - (\frac{1}{f s})}

Go Euler Load given Maximum Deflection for Columns with Initial Curvature

P E = \frac{P}{1 - (\frac{C}{δ c})}

Other formulas in Columns With Initial Curvature category

Go Value of Distance 'X' given Initial Deflection at Distance X from end A

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

Go Length of Column given Initial Deflection at Distance X from end A

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{π^{2} \cdot I}

Go Moment of Inertia given Euler Load

I = \frac{P E \cdot (l^{2})}{(π^{2}) \cdot ε column}

How to Evaluate Euler Load given Final Deflection at Distance X from end A of Column?

Euler Load given Final Deflection at Distance X from end A of Column evaluator uses Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)) to evaluate the Euler Load, The Euler Load given Final Deflection at Distance X from end A of Column formula is defined as a measure of the load that a column with initial curvature can withstand, taking into account the final deflection at a specific distance from the end of the column, providing a critical value for structural integrity assessment. Euler Load is denoted by P_E symbol.

How to evaluate Euler Load given Final Deflection at Distance X from end A of Column using this online evaluator? To use this online evaluator for Euler Load given Final Deflection at Distance X from end A of Column, enter Crippling Load (P), Maximum Initial Deflection (C), Distance of Deflection from end A (x), Length of Column (l) & Deflection of Column (δ_c) and hit the calculate button.

FAQs on Euler Load given Final Deflection at Distance X from end A of Column

What is the formula to find Euler Load given Final Deflection at Distance X from end A of Column?

The formula of Euler Load given Final Deflection at Distance X from end A of Column is expressed as Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)). Here is an example- 5710.916 = 2571.429/(1-(0.3*sin((pi*0.035)/5)/0.01847108)).

How to calculate Euler Load given Final Deflection at Distance X from end A of Column?

With Crippling Load (P), Maximum Initial Deflection (C), Distance of Deflection from end A (x), Length of Column (l) & Deflection of Column (δ_c) we can find Euler Load given Final Deflection at Distance X from end A of Column using the formula - Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)). This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Euler Load?

Here are the different ways to Calculate Euler Load-

Euler Load=((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)
Euler Load=Crippling Load/(1-(1/Factor of Safety))
Euler Load=Crippling Load/(1-(Maximum Initial Deflection/Deflection of Column))

Can the Euler Load given Final Deflection at Distance X from end A of Column be negative?

Yes, the Euler Load given Final Deflection at Distance X from end A of Column, measured in Force can be negative.

Which unit is used to measure Euler Load given Final Deflection at Distance X from end A of Column?

Euler Load given Final Deflection at Distance X from end A of Column is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Euler Load given Final Deflection at Distance X from end A of Column can be measured.

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Euler Load given Final Deflection at Distance X from end A of Column Formula

​GoEuler Load Formula

​GoEuler Load given Factor of Safety Formula

Euler Load given Final Deflection at Distance X from end A of Column Example

Euler Load given Final Deflection at Distance X from end A of Column Solution

Euler Load given Final Deflection at Distance X from end A of Column Formula Elements

Other Formulas to find Euler Load

Other formulas in Columns With Initial Curvature category

How to Evaluate Euler Load given Final Deflection at Distance X from end A of Column?

FAQs on Euler Load given Final Deflection at Distance X from end A of Column

Variable Name

GoEuler Load Formula

GoEuler Load given Factor of Safety Formula